If the normal to the curve $y=f(x)$ at $(1,2)$ makes an angle $\frac{3 \pi}{4}$ with the positive $X$-axis, then $f^{\prime}(1)=$

Let $\Gamma$ be the curve $y=b e^{-x/a}$ and $L$ be the straight line $\frac{x}{a}+\frac{y}{b}=1$, where $a, b \in \mathbb{R}$. Which of the following statements is true?

For a curve,what is the value of $\frac{(\text{Length of Normal})^2}{(\text{Length of Tangent})^2}$?

The equation of the normal drawn to the curve $y^3=4 x^5$ at the point $(4,16)$ is

If the tangent to the curve $xy + ax + by = 0$ at $(1, 1)$ makes an angle $\tan^{-1}(2)$ with the $x$-axis,then $\left( \frac{a + b}{ab} \right)$ is equal to:

The equation of the normal to the curve $y=x \log x$ parallel to $2x-2y+3=0$ is